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Uniform Asymptoti Integration of a Family of Linear Differential Systems
Author(s) -
Behncke Horst,
Remling Christian
Publication year - 2001
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200105)225:1<5::aid-mana5>3.0.co;2-k
Subject(s) - mathematics , differential (mechanical device) , calculus (dental) , mathematical analysis , medicine , engineering , aerospace engineering , dentistry
Consider a family of linear differential systems y ′ = A ( x, z ) y depending on a parameter z Assume, as in Levinson's Theorem, that A = Λ + R with Λ diagonal and R integrable. We discuss the problem of asymptotically solving this systemwith uniform (in z ) control on the error terms.Questions of this type occur in the spectral theory of differential operators.